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Is it true the number of elements in the sample space of an event is equal to the total number of possible outcomes?
true
What is the probability of getting a number greater than or equal to 2 when rolling a number cube numbered 1 to 6?
Probability is a ratio written as the number of desired outcomes divided by the number of possible outcomes. On a six-sided number cube, there are 5 chances of getting a number greater than or equal to 2 (2,3,4,5,6) and 6 possible outcomes (1,2,3,4,5,6) so your probability would be 5/6.
Is there a formula for probability problems?
Yes. The sum of the probabilities of all possible outcomes is equal to one. Given events that are equally likely to happen, the probability that any given outcome occurs will be equal to the number of specified outcomes, divided by the number of all outcomes. If events are not equally likely to happen - let's say that Bent-Nose Bill is holding a lottery - then the probability is considerably different. As Damon Runyan put it, "The race is not always to the swift, nor the battle to the strong, but that's the way to bet"
What is the probability of rolling a sum of more than 4 with two number cubes?
With two six-sided dice, there are 36 possible outcomes. Let's look at the outcomes which the sum is less than or equal to 4: {1.1 1.2 1.3 2.1 2.2 3.1} That's 6 outcomes, which leaves 30 outcomes with greater than 4. So 30/36 = 5/6 or 83.333%
What does it mean for a probability to be fair?
A probability is fair if there is no bias in any of the possible outcomes. Said another way, all of the possible outcomes in a fair distribution have an equal probability.
